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Question
Find the cube root of the following number by the prime factorisation method.
110592
Solution
| 2 | 110592 |
| 2 | 55296 |
| 2 | 27648 |
| 2 | 13824 |
| 2 | 6912 |
| 2 | 3456 |
| 2 | 1728 |
| 2 | 864 |
| 2 | 432 |
| 2 | 216 |
| 2 | 108 |
| 2 | 54 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factorisation of 110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
= 23 × 23 × 23 × 23 × 33
=(2 × 2 × 2 × 2 × 3)3
∴ `root3 (110592)`
= 2 × 2 × 2 × 2 × 3
= 48
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